Averaging of the Dirichlet problem for a special hyperbolic Kirchhoff equation

• Datum: 2006
• Hauptverfasser: Sidenko, N. R., Сиденко, Н. Р.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2006
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3449
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove a statement on the averaging of a hyperbolic initial-boundary-value problem in which the coefficient of the Laplace operator depends on the space $L^2$-norm of the gradient of the solution. The existence of the solution of this problem was studied by Pokhozhaev. In a space domain in $ℝ^n,\;...